Digital data compression robust relative to transmission noise

ABSTRACT

The invention concerns a digital data compression encoder, characterized in that it comprises: an input for a first data flow (S H ), and a second data flow (S L ), an encoding module, matching symbols of the first data flow, and code words, wherein, for certain symbols, there exist several words, called redundant, corresponding to the same symbol, and a processing module for encoding the symbols of the first data flow based on the correspondence, by selecting among the redundant words, on the basis of at least part of the second data flow.

The present application is a national phase of International Application No. PCT/FR03/002245, filed Jul. 16, 2003, which claims priority to French Patent Application No. 02/09287, filed Jul. 22, 2002 and French Patent Application No. 02/14964, filed Nov. 28, 2002, all herein, incorporated by reference in their entirety.

The invention relates to digital data compression, in particular for multimedia signals (audio, image, video, voice), and the robust transmission of this data on noisy networks, such as wireless and mobile communications networks.

To reduce the transmission rate of digital data, it is compressed, seeking at the same time to approach the theoretical maximum that specialists refer to as “signal entropy”. To do this, use is often made of statistical codes also termed variable length codes, for example Huffman codes. However, these codes have the drawback of being very, sensitive to transmission errors. Inversion of a bit can lead to de-synchronization of the decoder, which results in erroneous decoding of all the data following the position of the erroneous bit.

Existing solutions for the compression, transmission and decompression of multimedia signals over a network, to which further reference will be made, are based on the hypothesis that a certain quality of data transport service is guaranteed. In other words they assume that, by relying on the use of correction codes, the transport and link layers will make it possible to achieve a quasi-null residual error rate (i.e. seen by the compression and decompression application). But this hypothesis of quasi-null residual error rate no longer holds true when the channel characteristics vary over time (non-stationary charnels), in particular in wireless and mobile networks, and for a realistic complexity of the channel code. Furthermore, the addition of redundancy by correction codes leads to a reduction of the effective data rate.

There is therefore a need for solutions that are robust relative to transmission noise, i.e. that are little affected by the bit errors induced by this noise on the one hand, and which facilitate optimal use of the bandwidth (i.e. the capacity) of the network on the other hand.

The present invention proposes some advances in this area.

In one of its aspects, the invention discloses a digital data compression encoder, which includes:

-   -   an input (physical or otherwise) for a first data flow, and a         second data flow,     -   an encoding module, matching symbols of the first data flow and         code words, wherein, for certain symbols, there exist several         words, called redundant, corresponding to the same symbol, and     -   a processing module for encoding the symbols of the first data         flow based on the match, by selecting among the redundant words,         on the basis of at least part of the second data flow.

In various other aspects:

-   -   the code words can be of fixed length,     -   the processing module includes:         -   a function to calculate the current multiplexing capacity of             the first data flow, based on the coding table, and         -   a function to extract a multiplexed part from the second             data flow, determined on the basis of the current             multiplexing capacity, to be carried by said redundant             words.     -   the encoder includes a transformation of a binary flow into a         multi-valued variable flow, in particular using the         transformations described in Table C below.     -   as a variant, the encoder includes a transformation of a binary         flow into a multi-valued variable flow, in particular using a         generalized Euclidian decomposition based on a global variable         given by the formula (E9) described below.

In a first variant:

-   -   the encoding module includes a coding table and the processing         module includes:         -   a function for reading a multiplexing capacity of each             current symbol of the first data flow based on the coding             table, and         -   a function for extraction of a part of the second data flow             determined from the multiplexing capacity, to be carried by             said redundant words,     -   the coding table includes for each symbol an associated number         of code words equal to a power of 2.

In a second variant:

-   -   the encoding module includes a binary encoding tree containing,         for each symbol of the first data flow, a first code word part,         of variable length and shorter than a maximum length, and the         processing module includes:         -   a function to calculate the multiplexing capacity for each             current symbol of the first data flow based on the first             code word part of each symbol,         -   a function to extract a part of the second data flow             determined from the multiplexing capacity, to be carried by             said redundant words.     -   as a variant, each symbol comprises a sequence of symbols.

In a third variant:

-   -   each symbol includes a sequence of symbols, and the encoding         module includes an arithmetic encoder capable of calculating,         for a sequence of symbols of the first data flow, a first code         word part of variable length and shorter than a maximum length;         the processing module includes:         -   a function to calculate the multiplexing capacity for each             current symbol of the first data flow based on the first             code word part of each symbol,         -   a function to extract a part of the second data flow             determined from the multiplexing capacity for each symbol,             to be carried by said redundant words.

In the second and third variant, said part of the second data flow is concatenated to the first code word part up to the maximum code word length.

In a general manner:

-   -   the second data flow is pre-encoded.     -   the rest of the second data flow is concatenated to the         transmitted data.

The invention also discloses a decoder capable of performing the inverse or reciprocal operations relative to those of the encoder in its different aspects.

The invention also discloses a digital data compression method that includes the following steps:

-   a. establishing a match between symbols of the first data flow and     code words, wherein, for certain symbols, there exist several words,     termed redundant, corresponding to the same symbol, and -   b. encoding the symbols of a first data flow based on step a., by     selecting among the redundant words, on the basis of at least part     of a second data flow.

This method can incorporate other aspects of encoding.

In addition, the invention also discloses a digital data decompression process, including steps reciprocal to those of the compression process.

Other features and advantages of the invention will become apparent upon examination of the following detailed description together with the attached drawings in which:

FIG. 1 is a flow diagram illustrating a code creation method,

FIG. 2 is a diagram giving an overview of the encoding method in its principal variant,

FIG. 2A illustrates a simplified example of a multiplexed code, with four elements,

FIG. 2B illustrates a variant of the code constructed in FIG. 2A,

FIG. 3 illustrates a first embodiment of a detailed encoding method,

FIG. 4 illustrates an alternative embodiment of the method in FIG. 3,

FIG. 5 illustrates an example of the creation of a storage capacity by assigning several code words to a symbol, a data flow q being capable of being jointly stored, and

FIG. 6 or Table C illustrates transformations used in an example where the parameter f_(v) is equal to 5,

FIG. 7 illustrates another simplified example of a four-element multiplexed code,

FIG. 8 illustrates a general encoding method for FIGS. 3 and 4,

FIG. 9 illustrates a second embodiment of a detailed encoding method,

FIG. 10 illustrates a results table of a first variant of the second embodiment of the encoding method according to FIG. 9,

FIG. 11 illustrates an overview of a second variant of the second embodiment of the encoding method according to FIG. 9,

FIG. 12 illustrates an overview of a third variant of the second embodiment of the encoding method according to FIG. 9.

In addition:

-   -   Appendix 1 contains expressions used in the present description,         and     -   Appendix 2 contains natural language algorithms used in the         present description.

The drawings and the appendices essentially include elements that are certain in character. They will therefore serve not only to aid understanding of the description, but will also contribute to the definition of the invention, as applicable.

In a general manner, a compression system for multimedia signals (image, video, audio, voice) uses statistical codes also termed variable length codes. These make it possible to obtain data rates approaching what the specialists refer to as “signal entropy”. The codes most widely used in existing systems (particularly in the standards) are Huffman codes which have been described in the following paper: D. A. Huffman: “A method for the construction of minimum redundancy codes”, Proc. IRE, 40 (1951), p. 1098–1101.

More recently, there has been renewed interest in arithmetic codes owing to their increased performance in compression terms. In effect these codes make it possible to decouple the encoding method from the supposed source model. This facilitates the use of higher-order statistical models. These arithmetic codes have been described in research papers such as

-   J. J. Rissanen “Generalized kraft inequality and arithmetic”, IBM     J.Res. Develop., 20:198–203, May 1976 -   J. J. Rissanen, “Arithmetic coding as number representations”, Acta     Polytech. Scand. Math., 31:44–51, December 1979 and in American     patents U.S. Pat. Nos. 4,286,256, 4,467,317, 4,652,856.

Until recently, the design of compression systems was undertaken assuming a guaranteed quality of transport service. It was assumed in fact that the lower layers of the OSI model incorporate error correction codes ensuring a quasi-null residual error rate as seen by the application.

Variable length codes could therefore be widely used despite their considerable sensitivity to transmission noise. Any error in the binary train can cause de-synchronization of the decoder and therefore propagation of errors to the decoded information stream.

To mitigate this propagation problem, the first-generation standards (H.261, H.263, MPEG-1, MPEG-2) incorporated synchronization markers into the syntax of the transmitted binary train. These are long code words (16 or 22 bits composed of a string of 15 or 21 bits set to ‘1’ followed by a ‘0’) which cannot be emulated by errors occurring in the other code words and which can therefore be recognized by the decoder with a probability close to ‘1’.

This leads to the binary train being structured in packets delimited by these synchronization markers. This enables the propagation of errors to be confined within a packet. However if an error occurs at the start of the packet the rest of the packet may be lost. Moreover, the frequency of these synchronization markers must be restricted to avoid undue loss of compression efficiency.

This hypothesis of quasi-null residual error rate no longer holds true in wireless and mobile networks in which the channel characteristics vary over time (non-stationary channels). This residual error rate seen by the source signal decoder is often far from negligible.

The new standards (H.263+ and MPEG-4) then adopted reversible variable length codes (RVLC). A particular feature of these codes is that they can be decoded from the first to the last bit in a packet, and inversely from the last to the first bit in the packet.

If an error has occurred in the middle of a packet, this code symmetry makes it possible to confine the error propagation to a segment in the middle of the packet instead of propagating it to the end of the packet delimited by a synchronization marker. However, the code symmetry results in a loss of compression efficiency in the order of 10% compared with a Huffman code. In addition, reversible variable length codes do not completely overcome the problem of error propagation: if an error occurs at the start and end of a packet, the whole packet is liable to be erroneous.

The design of codes that are both efficient in compression terms (i.e. approaching entropy of the source) while at the same time being robust relative to transmission noise, is therefore an important goal, in particular for future multimedia (image, video, audio, voice) mobile communications systems. New standards are being developed for these systems both within the ITTU (International Telecommunication Union) and ISO (International Organization for Standardization).

Although standards play a predominant role in the telecommunications sector, such a family of codes could also find applications in niche markets calling for proprietary solutions.

In a general manner, the digital data compression methods proposed below are implemented by a digital data compression encoder according to the invention including an encoding module and a processing module.

More specifically, an encoding module establishes a match between symbols in a first data flow and code words, wherein for certain symbols there exist several words, termed redundant, corresponding to the same symbol. In a general manner, an encoding module can be any form of storage presenting the match defined above, any form of representation of this match, or any coding function calculating this match. Thus, by way of example only, the encoding module can be an encoding table, an encoding tree or an arithmetic encoder depending on the compression methods detailed below.

The processing module implements the stages of the data compression methods based on the first data flow and a second data flow and the encoding module. The processing module includes functions capable of performing certain steps in the processes and can include a transformation of a binary flow into a multi-valued variable flow. These functions include a function for calculating or reading a multiplexing capacity associated with the first data flow, and a function for extracting part of the second data flow. These functions will be developed more particularly in the rest of the description. In a symmetrical manner, the data decompression methods are implemented by a decoder according to the invention.

In a general manner, the method described below involves creating fixed length codes for higher priority source data (flow s_(H)), by assigning several code words to each possible representation of this source.

Thus, to transmit a symbol, it is possible to choose from the different possible representations of the latter. This choice, which is a multi-valued variable, defines a storage capacity that will be capable of being used to jointly transmit other data (Cf. example in FIG. 5 detailed below). These are data of lesser importance, represented by a flow denoted s_(L), which will be represented via multiple representation of the symbols.

FIG. 1 shows the method of creating these codes, more precisely the method of creating multiplexed codes.

At step 100, the higher priority source, s_(H), takes its values from an alphabet of Ω elements, which can be defined by formula (E1) attached. It is assumed that the probability law μ of occurrence of the symbols in this alphabet is known. The notation μ_(i) represents the probability associated with symbol a_(i) in the alphabet of the source s_(H), as represented by formula (E2).

The method of creating codes illustrated in FIG. 1 can then be broken down into 2 main steps:

-   -   For each symbol a_(i), selection of the number N_(i) of code         words assigned to this symbol,     -   Assignment of code words to the symbols.

The first step involves the selection of code parameters c and (N_(i)) broken down into different steps 120, 130, 140 and 150.

At step 120-1, a code word length parameter c, in number of bits, is chosen. In a first embodiment (in reference to FIGS. 2A and 5), the parameter c takes the value c=4. In another embodiment (in reference to FIGS. 2B, 7 and 10), the parameter c takes the value 3. This defines 2^(c) code words at step 120-2, to be allocated between the symbols of alphabet A.

Depending on the possible values of the probability μ_(i) at step 130-1, the alphabet A symbol set is partitioned into two subsets A_(m) and A_(M) respectively at step 130-2 and at step 130-3. The first is the symbol set a_(i) of which the probability μ_(i) is less than or equal to ½^(c), the second is its counterpart in A. The cardinals of these sets are respectively denoted Ω_(m), and Ω_(M).

At step 140, the probability law μ is then calculated on the symbols of A_(M). It is given by formula (E3).

At step 150-1, the number of code words per symbol is then chosen so as to verify approximately formula (E4), under the constraint of formula (E5) for the subset A_(M). A conventional optimization algorithm may be used for this purpose. At step 150-2, the number of code words per symbol is determined for the symbol set of alphabet A.

In a variant of the code creation method including steps 120, 130, 140 and 150, a further step is added after step 150, and steps 120-1 and 150-1 respectively take the following form.

Let f₁=2, f₂=3, f₃=5 . . . , f_(ν), ν be first prime numbers. In addition to parameter c at step, 120-1, a prime number f_(V) is also chosen from these prime numbers.

At step 150-1, the procedure is the same, but with the addition of a further constraint at step 150-11 on the choice of the number of code words N_(i) associated with each symbol: the decomposition into prime factors of all the N_(i) must not contain a prime factor greater than f_(V).

After step 150-1, the decomposition of each N_(i) into prime factors is then carried out, and for any N_(i) the number of times that each prime factor f_(j), with 1≦j≦v occurs in this decomposition is calculated. This number is denoted α_(i,j), where i denotes the symbol a_(i) considered and j denotes the prime number f_(j) considered. The correspondence between a_(i) and the numbers α_(i,l) . . . α_(i,v) can be stored in a table termed the “alpha table”.

The additional step entails allocating code words to the symbols. This step is broken down into different steps 160 and 180 described below.

At step 160, binary labeling (0000, 0001, . . . ) of the symbols arranged, by way of example only, in a lexicographic sequence is carried out. This make it possible to assign N_(i) code words to the different symbols, the parameter N_(i) being an integer determined at the preceding step (150-2). The set of code words thus associated with a symbol a_(i) is referred to as the a_(i) equivalence class, and denoted C_(i) at step 180.

A value between 0 and N_(i)−1, here referred to as a state, is then assigned to the code words of each equivalence class. This value identifies the code word within the equivalence class.

Thus, each code word c_(i) is associated with a symbol a_(i) and a state variable between 0 and N_(i)−1, as illustrated by the expression (E6).

An example of a code thus constructed is given in Table A, FIG. 2A for f_(v)=5 and c=4. For each symbol a_(i) in column 13-A, Table A includes a column 11-A including the classes C_(i), a column 12-A including the code words assigned to each class, a column 14-A including the numbers N_(i) of code words per class, a column 15-A including the probabilities μ_(i) associated with each class, and a column 16-A including a state q of each code word in a class. In this example, the symbols a_(i) include 4 elements of the alphabet.

A variant of the code constructed is given in Table B, FIG. 2B for f_(v)=2 and c=3. Table B defines a binary multiplexed code, i.e. a multiplexed code such that for any symbol a_(i) the cardinal N_(i) of the associated equivalence class is an integer power of 2. If we denote this power 1_(i), the cardinal N_(i) of the equivalence class verifies E(11). For each symbol a_(i) in column 13-B, Table B includes a column 11-B including the classes C_(i), a column 12-B including the code words assigned to each class, a column 14-B including the numbers N_(i) of code words per class. In this example, the state variable q does not exist but other elements are present and their function will be better understood by reading the description: a column 15-B includes the probabilities μ_(i) each assigned to a class, a column 18-B includes a number Di of bits capable of being stored, Di being associated with each class, a column 17-B includes a set U_(i) of Di bits for each code word in a class. In this example, the symbols a_(i) include 4 elements of the alphabet with i taking the values between 1 and 4.

The condition (E11) on the cardinals of the equivalence classes leads to the fact that the choice of a code word within an equivalence class makes it possible to store a whole number of bits equal to the base 2 logarithm of the cardinal of the equivalence class. This number of bits Di can therefore be written according to (E12). Di represents a multiplexing capacity of a given symbol. Tables A and B are encoding tables, also referred to as multiplexed code word tables or multiplexed code table.

In a third alternative embodiment, a binary multiplexed code can also be constructed from a binary encoding tree associated with a code word prefix, this prefix being of variable length and shorter than a maximum length being the height of the tree, such as the Huffman code presented in FIG. 7. The relationship “lower” is to be understood to mean “lower or equal”. The tree is first divided into two branches respectively taking the value 1 and the value 0. In a recurrent manner, each branch of the tree is divided into two branches respectively taking the value 0 and the value 1. The parameter c is given by the height of the tree, i.e. by the length of the longest prefix (in the example c=3) of the tree. An equivalence class C_(i) is defined by a set of fixed-length code words each having a common first part, termed common prefix. This common prefix is the part of the code word with variable length used to represent the symbol a_(i) and denoted in FIG. 7 by the path formed by the successive branches shown as a solid line. For certain solid-line paths representing a symbol a_(i), there remain a certain number of dotted-line paths each representing a second part of the code word termed suffix. The suffix of a code word defines the bit set Ui as indicated by an arrow in the drawing.

Thus, the encoding tree is defined as an encoding module, matching the symbols of the priority data flow and code words, wherein for certain symbols there exist several words, termed redundant, corresponding to the same symbol. These code words are of fixed length and include a first and a second code word part, for example a prefix and a suffix of variable lengths. In a variant, the first and the second code word part can correspond respectively to the suffix and prefix of the code word. More generally, a code word can include several code parts.

FIGS. 2 and 3 illustrate the coding method, also termed encoding.

The encoding method is broken down as follows:

-   -   steps 1: the data flow of lower importance s_(L) at step 1-1 is         encoded in a binary sequence b=(b₁, b₂, . . . , b_(KB)) using a         reversible encoding at step 1-2. For this purpose, a Huffman         type reversible encoder or arithmetic encoder (non restrictive)         can be used. This gives rise to the generation of a sequence of         bits, denoted b at step 1-3.     -   steps 2: from the sequence of symbols s₁, s₂, . . . , s_(KH) of         the flow s_(H) at step 2-1 and reading the table of multiplexed         code words at step 2-2, the associated values n₁, n₂, . . . ,         n_(KH) are derived at step 2-3. For example, for a symbol s₁         corresponding to the symbol a_(i) in a table of multiplexed code         words, n₁, takes the value of N_(i) corresponding to the         representation of the symbol a_(i).     -   steps 3: the value Λ, is derived, here using formulae (E7) at         step 3-1. The number K′_(B) of bits which it will be possible to         store using the intrinsic redundancy of the multiplexed codes is         calculated using formula (E8) at step 3-2. This number K′_(B) of         bits, represents the multiplexing capacity of the flow s_(H) for         this encoding method.     -   steps 4: on condition that K_(B)<K_(B′) at step 4-1, K′_(B) bits         of flow b, for example the last K′_(B) bits of flow b (steps         4-2, 4-3) are used to calculate (step 4-4) a long integer γ         (step 4-5), given here by formula (E9). This corresponds to the         transformation of the last K′_(B) bits of the binary flow into a         global variable. If the condition K_(B)<K_(B′) is not verified         at step 4-1, the process resumes at step 2-1 by reducing the         value K_(H) (step 4-11).     -   steps 5: the value γ can then be used to calculate the states         q_(t), 1≦t≦K_(H) (step 5-2), using for example a generalized         Euclidian decomposition method (step 5-1), as illustrated in the         attached algorithm (A1). This involves generating a flow of         states q_(t), q_(t) being a multi-valued variable.     -   steps 6: for any t such that 1≦t≦K_(H), knowing the symbol s_(t)         and the state q_(t) calculated at the preceding step enables the         code word to be chosen from the table of multiplexed code words         (step 6-1). The multiplexed flow m is obtained including the         code words m₁ to M_(KH) (step 6-2).     -   steps 7: the K_(B)–K′_(B) bits of the flow of lower importance         (step 7-1) are then concatenated to the sequence of multiplexed         code words previously constructed (step 7-2) to form the         transmitted flow (step 7-3).

At least step 3 is implemented by the calculation function of the processing module. Steps 4, 5 and 6 at least are implemented by the extraction function of the processing module.

In a general manner, for an encoding method, an associated decoding process is carried out by performing operations that are the reverse of those of the encoding method.

A variant of the encoding method is illustrated in FIG. 4 and avoids performing calculations on long integers. The variant of the encoding method is broken down as follows:

-   -   steps 21 these correspond to steps 1 in FIG. 3     -   steps 22: these correspond to steps 2 in FIG. 3.     -   steps 23: the total number of times that each prime factor f_(j)         appears in the set of decompositions into factors of the         sequence of variables N_(t) is then determined from the         so-called “alpha” table (steps 23-1 and 23-2). This number is         denoted d_(j) below, and represents the number of f_(j)-valued         variables that can be multiplexed with the flow s_(H). Thus, for         each prime factor f_(j), d_(j) represents the sum of α_(t,j) in         the sequence of variables n_(t).     -   steps 24: the transformations that will be used to transform the         binary train into these f_(j)-valued variables are then chosen         (step 24-1). These transformations depend on the value of f_(v)         chosen. The transformations used for f_(v)=5 are presented in         Table C of FIG. 5.

They are presented in the form illustrated in the attached formulas (E10).

Thus, each transformation Tz takes u_(Tz) bits at the input (denoted below U_(T) by simplification for a given z) and transforms them respectively into v_(T,1), v_(T,2), . . . , v_(T, ν)variables 2, 3, 5, . . . , f_(v)-valued. In the example in Table C for f_(v)=5, each transformation Tz in column 31 takes u_(T) bits in column 32 as input and transforms them respectively into v_(T,1), v_(T,2), v_(T,3) variables 2, 3, 5-valued in columns 33, 34, 35. The required number of variables of each type is known: for each type of variable f_(j), it is d_(j) (Cf. step 23-2).

The attached algorithm A2 can be used to calculate the number g_(Tz) of times that the transformation T z must be used (step 24-2), for a variable z ranging from 0 to z_(max). (It is assumed that the transformations are arranged in descending order of relevance in the table).

-   -   step 25: K_(B′), the number of multiplexed bits, is calculated         by obtaining the product of the number of times g_(Tz) that a         transformation Tz must be used and the number of bits u_(T) at         the input of the transformation and adding these products         together for all the transformations z used. This number K′_(B)         of bits represents the multiplexing capacity of the flow s_(H)         for this encoding method. This step 25 corresponds to steps 3 in         FIG. 3. The following steps 26-1, 26-2, 26-3, and 26-11         correspond to steps 4-1, 4-2, 4-3 and 4-11 in FIG. 3.     -   steps 27: having chosen the number of transformations of each         type to be used, they are applied to the end of the binary flow         b (step 27-1).

For each transformation Tz, the u_(T) input bits are seen as the binary representation of an integer e.

This integer is then decomposed into several f_(j)-valued variables, as indicated in the formulas (E10). These variables are denoted e_(r,j), where:

-   j indicates that the value obtained is the representation of an     f_(j)-valued variable, and -   r indicates the number of the f_(j)-valued variable.

Values of e_(r,j) can be obtained from e using the method of algorithm A3. This algorithm is reiterated a number g_(Tz) of times for each transformation Tz.

On completion of this step 27-1, the results obtained are presented in the form of formulas (E10) and are concatenated so as to obtain v sequences of available variables (step 27-2):

-   -   the first, denoted F₁, is a sequence with a length d₁ of         2-valued variables (bits),     -   the j-th, denoted F_(j), is a sequence with a length d_(j) of         f_(j)-valued variables. Position pointers, denoted t_(j), are         assigned to the sequences, and are initially positioned at the         start of each sequence.     -   steps 28: the flow of states (step 28-1) is calculated from         these variables, the result of which is (step 28-2):

-   q=(q₁, q₂, . . . , q_(KH)).

This calculation may be performed by proceeding as follows:

-   -   for any t such that 1≦t≦K_(H), and thus for each symbol s_(t),         the decomposition into prime factors of n_(t) makes it possible         to determine the number α_(tj) of variables of each type         (2-valued, . . . , f_(j)-valued, . . . , f_(v)-valued, j ranging         from 1 to ν). Each sequence F_(j) previously obtained is divided         into K_(H) successive segments comprising α_(tj) bits for t         ranging from 1 to K_(H). The process is reiterated for j ranging         from 1 to ν. Each n_(t)-valued variable (q_(t)) is obtained by         the reciprocal process of iterative Euclidian decomposition,         applied to the segments F_(tj) of f_(j)-valued variables. An         example of implementation of this process is described by         algorithm A4. It will be noted that at the end of these steps         28, all the variables of the flows F_(j) have been used.     -   steps 29: for any t such that 1≦t≦K_(H), knowing the symbol         s_(t) and the state q_(t) calculated at the preceding step         enables the code word to be chosen from the table of multiplexed         code words (step 29-1). The multiplexed flow m is then obtained         (step 29-2).     -   steps 30: the K_(H)–K′_(H) bits of the flow of lower importance         (step 30-1) are then concatenated to the sequence of multiplexed         code words previously evaluated (step 30-2). The transmitted         flow is obtained (step 30-3).

At least step 25 is implemented by the calculation function of the processing module. At least step 27 is implemented by the extraction function of the processing module.

The encoding methods presented in reference to FIGS. 2, 3 and 4 can be generalized according to the encoding process in FIG. 8:

-   -   based on the table of multiplexed code words and the sequence of         symbols s_(H), the associated values n₁, n₂, . . . , n_(KH) are         calculated so as to calculate the multiplexing capacity K′_(B)         of the sequence of symbols s_(H) at step I.     -   the pre-encoded flow b is divided into two parts b′ and b″ at         step II in relation to the multiplexing capacity K′_(B),     -   the part b′ of the flow is transformed into a series of states q         using the values n₁, n₂, . . . . , n_(KH) at step V,     -   based on this series of states q and the table of multiplexed         code words, the multiplexed code words are selected at step VII,     -   these code words are assembled to form a multiplexed flow m at         step VIII,     -   the concatenated part b″ of the flow b is concatenated with the         multiplexed flow m at step IX.

At least step I is implemented by the calculation function of the processing module. At least step II is implemented by the extraction function of the processing module.

An example of the creation of a storage capacity according to the invention is illustrated in FIG. 5. Thus, for each symbol s_(t) in the data flow s_(H) a corresponding class C_(t) and the associated code words C_(t,q) are assigned relative to an encoding table. Each state q_(t) of a data flow q can be jointly stored after selection of the code word c_(t,qt) from the table of multiplexed code words.

In the case of conversion of the lower priority binary train, the variant of the encoding method with f_(v)=2 can be used. Another variant described below in reference to FIG. 9 can advantageously be used. Table B in FIG. 2B is used in this example.

The part of the conversion process for the binary train therefore consists of the following steps:

-   -   step 40: corresponds to steps 1 in FIG. 3.     -   step 42: The associated value D_(t) is derived by reading the         symbol s_(t) and reading the table of binary multiplexed codes.         This value D_(t) corresponds to the number of bits that can be         jointly encoded with s_(t). D_(t) is a multiplexing capacity of         a given symbol.     -   step 44: the next D_(t) bits of the pre-encoded binary train b         are read. It will be noted that the binary train is read         progressively in relation to a positioning pointer. These next         D_(t) bits are denoted u_(t) and play the same role as the         states (q_(t)).     -   step 46: the code word c_(st), ut is selected from the table of         binary multiplexed codes as a function of the symbol s_(t) and         the bits u_(t) , the table being indexed by a_(i) and U_(i) .         This code word is transmitted on the channel,     -   step 48: for each symbol s_(t) of the flow s_(H), with t in the         range from 1 to K_(H) steps 42 to 46 are performed.

At least step 42 is implemented by the calculation function of the processing module. At least step 44 is implemented by the extraction function of the processing module.

By way of an example of application of the process in FIG. 9, the highest priority sequence to be transmitted s_(H)=a_(H) a₂ a₂ a₃ a₂ a₁ a₂ a₄ a₁ a₂, of length K_(H)=10, and the low priority pre-encoded binary train b=0101010101010, are considered. The number of bits that can be multiplexed with each representation of s_(H) is given, for t ranging from 1 to K_(H), by (D_(t))=(1, 2, 2, 0, 2, 1, 2, 0, 1, 2). The number of bits d_(t) in the binary train b is read progressively for t ranging from 1 to K_(H) so as to obtain the sequences u_(t) of bits ( u₁ , . . . , u_(KH) )=(0, 10, 10, ø, 10, 1, 01, ø, 0, 10). Then, for any t, the combination (a_(t), u_(t) ) indexes a code word in the binary multiplexed code table. The binary train effectively transmitted is 000 100 100 110 001 011 111 000 100.

As a variant, the process in FIG. 9 can also use the encoding tree. In this variant, steps 42 to 46 take the following form:

-   -   step 42: by reading the symbol S_(t) and reading the binary         encoding tree, the code word prefix for the symbol s_(t) is         obtained. The number of bits in this prefix is used to derive         the number of bits D_(t) that can be jointly encoded with s_(t)         to form a sequence of bits having a total length equal to the         height of the encoding tree. D_(t) is a multiplexing capacity of         a given symbol.     -   step 44: the next D_(t) bits of the pre-encoded binary train b         are read. It will be noted that the binary train is read         progressively in relation to a positioning pointer. These next         D_(t) bits are denoted u_(t) .     -   step 46: the code word transmitted on the channel results from         the concatenation of the code word prefix for the symbol s_(t)         and the bits u_(t) of the binary train b. Thus, utilization of         the binary train b enables a choice to be made between the         possible code words shown as dotted lines on the encoding tree         in FIG. 7 for a given symbol.

At least step 44 is implemented by the extraction function of the processing module.

By way of example, using the sequence s_(H) and the binary train b indicated previously in the case of FIG. 10 and the encoding tree in FIG. 7 to determine the code word prefixes, the code word flow m_(t) is obtained by concatenation of the prefixes and suffixes u_(t) .

In a general manner, the encoding tree makes it possible to define a code word prefix for each symbol in the flow s_(H), which is equivalent to defining several possible code words for certain symbols. The choice between these possible code words will be made once the binary code to determine the code word suffix has been read and the code word has been formed by concatenation of the prefix and suffix. Calculation of the sum of the set of D_(t) associated with the symbols forming the flow s_(H) makes it possible to determine the multiplexing capacity of the flow s_(H).

Other variants of the encoding method are illustrated below in reference to FIGS. 11 and 12.

It may be useful to consider creating a multiplexed code not on the alphabet but on a “product alphabet”. The term “product alphabet”, refers to an alphabet composed not of symbols but sequences of symbols. In the example in FIG. 11, the source s_(H) 50 comprises K symbols. It is converted into a C-uplet source denoted H (of length K/C these C-uplets being designated H1, H2, H3, . . . H_(K/C) and respectively numbered 51, 52, 53 and 55. Any C-uplet of symbols has the probability of occurrence (E13). It is used to derive the calculation of the probability distribution μ_(H) associated with the C-uplets. The binary encoding tree (termed “product binary encoding tree”) is created by considering, for each C-uplet, the probabilities of occurrence of each sequence of length C given in (E13). The code word prefix associated with a sequence of symbols is read from the encoding tree.

According to FIG. 11, for each sequence of symbols the multiplexing function 62 comprises a certain number of functions performing the steps corresponding to the variant process in FIG. 9. At each step, the “symbol” is replaced by a “sequence of symbols”. Thus, the encoding method using an encoding tree is applied directly to the C-uplet representations of the source H.

If alphabet A is too large to be able to use an encoding tree, it is also possible to replace “the product encoding tree” by an arithmetic code as illustrated in FIG. 12. Thus, the source s_(H) 70 is divided into C-uplets, which leads to a number of C-uplets equal to K/C. These C-uplets can be relatively long and are encoded by independent arithmetic (non restrictive) encoders. In the example in FIG. 12, each C-uplet is encoded by a separate arithmetic encoder 71, 72, 73 and 75. The output of these arithmetic encoders consists of sequences H₁, H₂, H_(K/C) of variable length bits numbered 81-1, 82-1, 85-1. The length c of the code words corresponds to the longest possible sequence of bits Ht at the output of the arithmetic encoders. Each sequence of bits is then seen as a code word prefix. For each prefix of length strictly shorter than the length c, there exist several code words of length c corresponding to the same symbol.

The formation of a code word is the same as in the “product alphabet” variant. Thus, the encoded binary flow b numbered 90 is read progressively to form the suffixes 81-2, 82-2, 85-2 thereby complementing the prefixes 81-1, 82-1, 85-1 and forming the multiplexed code words. If the number K/C is not an integer, the last C′=K−C [K/C] symbols form a C′-uplet which is encoded arithmetically.

As indicated for FIG. 9, the number of bits in a prefix is used to derive the number of bits D_(t) (1<t<K) that can be jointly encoded with H_(t) to form a sequence of bits having a total length equal to the height of the encoding tree. D_(t) is a multiplexing capacity of a given sequence of symbols. Calculation of the sum of the set of D_(t) associated with the symbol sequences forming the source H makes it possible to determine the multiplexing capacity of the flow s_(H).

In a general manner, an arithmetic encoder or an encoding tree can be used to establish a code word prefix for each, sequence of symbols, which is equivalent to defining several possible code words for certain symbol sequences. The choice between these possible code words will be made once the binary code to determine the code word suffix has been read and the code word has been formed by concatenation of the prefix and suffix.

Thus, the invention allows multiplexing of two data flows s_(H) and s_(L), in order to reduce the error sensitivity of one of them s_(H), designated as more important or higher priority. These two flows can be differentiated in the same signal source, in particular as in the following examples of s_(H) and s_(L) sources:

-   -   low frequencies and high frequencies extracted by         multi-resolution decomposition (filter banks, wavelet         transforms) of a signal,     -   texture information (e.g. DCT coefficients, wavelet         coefficients) and movement information,     -   most significant bits and least significant bits of wavelet         coefficients or quantified samples of a signal.

Of course, the above enumeration is in no way exhaustive.

Furthermore, in that the code words are of fixed length (or if synchronization markers are used), the invention can be used to create a multiplexed code capable of jointly describing two flows, at least one of which has the benefit of perfect synchronization.

Appendix 1—Formulas

$\begin{matrix} {A = \left\{ {\alpha_{1},\ldots\mspace{11mu},\alpha_{i},\ldots\mspace{11mu},\alpha_{\Omega}} \right\}} & ({E1}) \\ {\mu_{i} = {P\left( a_{i} \right)}} & ({E2}) \\ {\;{{\overset{\sim}{\mu}}_{i} = {\frac{2^{c}}{2^{c} - \Omega_{M}}\mu_{i}}}} & ({E3}) \\ {N_{i} = {\left( {2^{c} - \Omega_{m}} \right) \star {\overset{\sim}{\mu}}_{i}}} & ({E4}) \\ {{\sum\limits_{i \in A}N_{i}} = 2^{c}} & ({E5}) \\ \left. c_{i,j}\rightleftarrows\left( {s_{i},q_{j}} \right) \right. & ({E6}) \\ {\Lambda = {\prod\limits_{t = 1}^{K_{H}}\; n_{t}}} & ({E7}) \\ {K_{B}^{\prime} = \left\lfloor {\log_{2}(\Lambda)} \right\rfloor} & ({E8}) \\ {\gamma = {\sum\limits_{r = 1}^{K_{H}}{b_{r + K_{B} - K_{B}^{\prime}}{2^{4 - 1}.}}}} & ({E9}) \\ \left. {u_{\tau}{bits}}\rightleftarrows\left\{ \begin{matrix} {\upsilon_{\tau,1}2\text{-}{valued}\mspace{14mu}{variables}} & {e_{1,1},e_{2,1},\ldots\mspace{11mu},e_{\upsilon_{\tau,1},1}} \\ {\upsilon_{\tau,2}3\text{-}{valued}\mspace{14mu}{variables}} & {e_{1,2},e_{2,2},\ldots\mspace{11mu},e_{\upsilon_{\tau,2},2}} \\ \ldots & \; \\ {\upsilon_{\tau,1}{fvi}\text{-}{valued}\mspace{14mu}{variables}} & {e_{1,\upsilon},e_{2,\upsilon},\ldots\mspace{11mu},e_{\upsilon_{\tau,\upsilon},\upsilon}} \end{matrix} \right. \right. & ({E10}) \\ {{\forall{i\; \in \left\lbrack {1\mspace{11mu}\ldots\mspace{11mu}\Omega} \right\rbrack}},{{\exists\;{l_{i} \in {{\mathbb{N}}/N_{i}}}} = 2^{l_{i}}}} & ({E11}) \\ {D_{i} = {{\log_{2}\left( N_{i} \right)} = {c - l_{i}}}} & ({E12}) \\ {{P\left( {S_{t}S_{t + 1}\mspace{11mu}\ldots\mspace{11mu} S_{t + C - 1}} \right)} = {{P\left( S_{t} \right)}{P\left( {S_{t + 1}/S_{t}} \right)}\mspace{11mu}\ldots\mspace{11mu}{P\left( {S_{t + C - 1}/S_{t + C - 2}} \right)}}} & ({E13}) \end{matrix}$ Appendix 2—Algorithms

$A\; 1{{\begin{matrix} {\gamma^{\prime} = \gamma} \\ {{{For}\mspace{14mu} t} = {1:K_{H}}} \\ {q_{t} = {\gamma^{\prime}\mspace{14mu}{modulo}\mspace{14mu} n_{t}}} \\ {\gamma^{\prime} = \frac{\gamma^{\prime} - {q\;}_{t}}{n_{t}}} \\ {{End}\mspace{14mu}{for}} \end{matrix}A\; 2{{\begin{matrix} {z = 0} \\ {{\%\mspace{14mu}{while}\mspace{14mu}{fj}} - {{valued}\mspace{14mu}{variables}\mspace{14mu}{remain}\mspace{14mu}{to}\mspace{14mu}{be}\mspace{14mu}{obtained}}} \\ {{{While}\mspace{14mu}{sum}\mspace{14mu}\left( d_{j} \right)} > 0} \\ {\begin{matrix} {\%\mspace{14mu}{Calculate}\mspace{14mu}{the}\mspace{14mu}{number}\mspace{14mu}{of}\mspace{14mu}{times}\mspace{14mu}{that}\mspace{14mu}{the}\mspace{14mu}{transformation}\mspace{14mu}\tau_{z}\mspace{14mu}{is}\mspace{14mu}{used}} \\ {{g\;\tau_{z}} = {{{floor}\mspace{14mu}\left( {\min\;\left( \frac{d_{j}}{\upsilon_{\tau_{z,j}}} \right)} \right)\upsilon_{\tau_{z,j}}} \neq 0}} \\ {{\%\mspace{14mu}{Calculate}\mspace{14mu}{the}\mspace{14mu}{number}\mspace{14mu}{of}\mspace{14mu} f_{j}} - {{valued}\mspace{14mu}{variables}}} \\ {\%\mspace{14mu}{which}\mspace{14mu}{have}\mspace{14mu}{not}\mspace{14mu}{been}\mspace{14mu}{transformed}\mspace{14mu}{by}\mspace{14mu}{the}\mspace{14mu}{transformation}\mspace{14mu}\tau_{z}} \\ {{For}\mspace{14mu}{each}\mspace{14mu} j\mspace{14mu}{between}\mspace{14mu} 1\mspace{14mu}{and}\mspace{14mu} v} \\ {\begin{matrix} {d_{j} = {d_{j} - {{g\;\tau_{z}} \star \upsilon_{\tau_{z,j}}}}} \\ {\%\mspace{14mu}} \\ {z = {z + 1}} \end{matrix}} \end{matrix}} \end{matrix}A\; 3{{\begin{matrix} {e^{\prime} = e} \\ {{{For}\mspace{14mu} j} = {1\text{:}v}} \\ {{{For}\mspace{14mu}\tau} = {1\text{:}\upsilon_{\tau,j}}} \\ {e_{r,j} = {e^{\prime}\mspace{14mu}{modulo}\mspace{14mu} f_{j}}} \\ {e^{\prime} = \frac{e^{\prime} - e_{r,j}}{f_{j}}} \\ {{End}\mspace{14mu}{for}} \\ {{End}\mspace{14mu}{for}} \end{matrix}A\; 4{{\begin{matrix} {{{For}\mspace{14mu} j} = {1\text{:}v}} \\ {{tj} = 1} \\ {{End}\mspace{14mu}{for}} \\ {{{For}\mspace{14mu} t} = {1\text{:}K_{H}}} \\ {q_{t} = 0} \\ {{{For}\mspace{14mu} j} = {{v\text{:}1\mspace{14mu}{by}}\mspace{14mu} - 1}} \\ {{{For}\mspace{14mu}\tau} = {1\text{:}\alpha_{t,j}}} \\ {{qt} = {{q_{t} \star f_{j}} + {F_{j}\left( t_{j} \right)}}} \\ {{tj} = {{tj} + 1}} \\ {{End}\mspace{14mu}{for}} \\ {{End}\mspace{14mu}{for}} \\ {{End}\mspace{14mu}{for}} \end{matrix}.}}}}}}}}$ 

1. Digital data compression encoder, characterized in that it includes: an input for a first data flow (s_(H)), and a second data flow (s_(L)), an encoding module, matching symbols of the first data flow and code words, wherein, for certain symbols, there exist several words, called redundant, corresponding to the same symbol, and a processing module for encoding the symbols of the first data flow based on the match, by selecting among the redundant words, on the basis of at least part of the second data flow.
 2. Encoder according to claim 1, characterized in that the code words are of fixed length.
 3. Encoder according to claim 1, characterized in that the processing module includes: a function to calculate the current multiplexing capacity of the first data flow (s_(H)), based on the encoding module, and a function to extract a multiplexed part from the second data flow (s_(L)), determined on the basis of the current multiplexing capacity, to be carried by said redundant words.
 4. Encoder according to claim 1, characterized in that it includes a transformation of a binary flow into a multi-valued variable flow.
 5. Encoder according to claim 4, characterized in that it includes a transformation of a binary flow into a multi-valued variable flow, in particular using the transformations described in Table C.
 6. Encoder according to claim 5, characterized in that it includes a transformation of a binary flow into a multi-valued variable flow, in particular using a generalized Euclidian decomposition based on a global variable given by the relationship (E9).
 7. Encoder according to claim 1, characterized in that the encoding module includes an encoding table and in that the processing module includes: a function to read a multiplexing capacity of each current symbol of the first data flow (s_(H)) based on the encoding table and a function to extract a part of the second data flow (s_(L)) determined from the multiplexing capacity, to be carried by said redundant words.
 8. Encoder according to claim 7, characterized in that the encoding table includes, for each symbol, an associated number of code words equal to a power of
 2. 9. Encoder according to claim 1, characterized in that the encoding module includes a binary encoding tree containing, for each symbol in the first data flow, a first code word part, of variable length and shorter than a maximum length, and in that the processing module includes: a function to compute the multiplexing capacity for each current symbol of the first data flow (s_(H)) based on the first code word part of each symbol, a function to extract a part of the second data flow (s_(L)) determined from the multiplexing capacity, to be carried by said redundant words.
 10. Encoder according to claim 9, characterized in that each symbol comprises a sequence of symbols.
 11. Encoder according to claim 9, characterized in that said part of the second data flow is concatenated with the first code word part up to the maximum length of the code word.
 12. Encoder according to claim 1, characterized in that each symbol comprises a sequence of symbols, in that the encoding module includes an arithmetic encoder designed to calculate, for a symbol sequence in the first data flow, a first code word part of variable length and shorter than a maximum length, and in that the processing module includes: a function to calculate the multiplexing capacity for each current symbol of the first data flow (s_(H)) based on the first code word part of each symbol, a function to extract a part of the second data flow (s_(L)) determined from the multiplexing capacity for each symbol, to be carried by said redundant words.
 13. Encoder according to claim 1, characterized in that the second data flow is pre-encoded.
 14. Encoder according to claim 1, characterized in that the rest of the second data flow is concatenated with the transmitted data.
 15. Decoder designed to perform the inverse operations relative to those of the encoder according to claim
 1. 16. Digital data compression method, characterized by: a. establishing a match between symbols of the first data flow and code words, wherein, for certain symbols, there exist several words, termed redundant, corresponding to the same symbol, and b. encoding the symbols of a first data flow based on the match obtained at step a., by selecting among the redundant words, on the basis of at least part of a second data flow, characterized by sub-functions according to claim
 1. 17. Digital data compression method, characterized by the following steps: a. establishing a match between symbols of the first data flow and code words, wherein, for certain symbols, there exist several words, termed redundant, corresponding to the same symbol, and b. encoding the symbols of a first data flow based on the match obtained at step a., by selecting among the redundant words, on the basis of at least part of a second data flow.
 18. Digital data decompression method, characterized by steps reciprocal to those of the method according to claim
 17. 